The 1994 Group, which represents top institutions such as York, Durham, Exeter, Lancaster and St Andrews, said that the existing £3,200-a-year cap should be lifted to “enhance excellence in learning and teaching”.

It said that fees for the poorest students should be subsidised, suggesting higher costs for those from middle-class backgrounds.

Universities should also be able to charge more for the most expensive or sought-after courses, it was claimed. This would lead to a rise in fees for those students taking subjects such as medicine or law.

Professor Paul Wellings, 1994 Group chairman and vice-chancellor of Lancaster University, said: “Quality can only be maintained by a combination of increasing both institutional autonomy and funding. If the aim is to enhance quality, then a staged increase in the fee level above the baseline would be needed.”